Expanded solution (takes table schema into account):
-- Drop default contstraint for SchemaName.TableName.ColumnName
DECLARE @schema_name NVARCHAR(256)
DECLARE @table_name NVARCHAR(256)
DECLARE @col_name NVARCHAR(256)
DECLARE @Command NVARCHAR(1000)
set @schema_name = N'SchemaName'
set @table_name = N'TableName'
set @col_name = N'ColumnName'
SELECT @Command = 'ALTER TABLE [' + @schema_name + '].[' + @table_name + '] DROP CONSTRAINT ' + d.name
FROM sys.tables t
JOIN sys.default_constraints d
ON d.parent_object_id = t.object_id
JOIN sys.schemas s
ON s.schema_id = t.schema_id
JOIN sys.columns c
ON c.object_id = t.object_id
AND c.column_id = d.parent_column_id
WHERE t.name = @table_name
AND s.name = @schema_name
AND c.name = @col_name
EXECUTE (@Command)